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parallax

parallax (pâr´əlăks), any alteration in the relative apparent positions of objects produced by a shift in the position of the observer. In astronomy the term is used for several techniques for determining distance. Trigonometric parallax is the apparent displacement of a nearby star against the background of more distant stars resulting from the motion of the earth in its orbit around the sun. Formally, the parallax of a star is the angle at the star that is subtended by the mean distance between the earth and the sun. A shift in the angular position of a star will be greatest when observed at intervals of six months; this makes the parallax equal to the value of one half of the semiannual displacement of the star. If a star's parallax can be measured, it then determines the distance to the star. A unit of stellar measurement is the parsec; it is the distance at which a star would have a parallax of one second of arc and is equivalent to 206,265 times the distance from the earth to the sun, or about 3.3 light-years. A star's distance d in parsecs is the reciprocal of its parallax p (or d = 1/p). The first stellar parallax was measured in 1838 by Friedrich Bessel for the star 61 Cygni. Its parallax of 0.3 places it at a distance of 3.3 parsecs or about 11 light-years. The technique of stellar parallax is useful for stars within 100 parsecs. Spectroscopic parallax is the most widely used technique for determining the distances of stars that are too distant for their stellar parallaxes to be measured. From the analysis of a star's spectrum, its position on the Hertzsprung-Russell diagram is determined. This diagram correlates the spectral class of the star with its absolute magnitude. By comparing the absolute magnitude to its apparent brightness, the star's distance is calculated. Dynamical parallax is a method for determining the distance to a visual binary star. The angular diameter of the orbit of the stars around each other and their apparent brightness are observed. By applying Kepler's laws and the mass-luminosity relation, the distance of the binary star can be determined. Geocentric parallax is a technique similar to stellar parallax, which uses the diameter of the earth rather than the diameter of its orbit as a baseline. Because this baseline is relatively small, the technique is useful only for close celestial objects such as the moon or the asteroids.

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parallax

par·al·lax / ˈparəˌlaks/ • n. the effect whereby the position or direction of an object appears to differ when viewed from different positions, e.g., through the viewfinder and the lens of a camera. ∎  the angular amount of this in a particular case, esp. that of a star viewed from different points in the earth's orbit. DERIVATIVES: par·al·lac·tic / ˌparəˈlaktik/ adj.

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parallax

parallax Angular distance by which a celestial object appears to be displaced with respect to more distant objects, when viewed from opposite ends of a baseline. The parallax of a star (annual parallax) is the angle subtended at the star by the mean radius of the Earth's orbit (one astronomical unit); the smaller the angle, the more distant the star. See also parsec

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parallax

parallax XVII. — F. parallaxe — Gr. parállaxis change, alternation, mutual inclination of two lines meeting in an angle, f. parallássein, -allakt- alter, alternate, f. PARA-1 + allássein exchange, f. állos other.
So parallactic XVII. — Gr.

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parallax

parallax The apparent change in position of an object in relation to another when the viewpoint is changed. See also STEREOPTIC VISION.

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parallax

parallaxaxe (US ax), Backs, Bax, fax, flax, lax, max, pax, Sachs, sax, saxe, tax, wax •co-ax • addax • Fairfax • Ceefax •Halifax • Telefax • Filofax • banjax •Ajax •pickaxe (US pickax) • gravlax •gravadlax • poleaxe • toadflax •parallax •battleaxe (US battleax) •minimax • climax • Betamax • anthrax •hyrax •borax, storax, thorax •syntax • surtax • beeswax • earwax •Berks, Lourenço Marques, Marks, Marx, Parks, Sparks •annex, convex, ex, flex, hex, perplex, Rex, sex, specs, Tex, Tex-Mex, vex •ibex • index • codex • tubifex •spinifex • pontifex • Telex • triplex •simplex • multiplex •ilex, silex •complex • duplex • circumflex • Amex •annexe • Kleenex • apex • Tipp-Ex •haruspex • perspex • Pyrex •Durex, Lurex, murex •Middlesex • unisex • Semtex • latex •cortex, Gore-tex, vortex •vertex • Jacques •breeks, idée fixe, maxixe, Weeks

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Parallax

Parallax

How parallax works

Parallax measurements

Resources

Parallex, in astronomy, is the apparent shift (that is, change of angular position) of two stationary objects relative to each other as perceived by an observer whose position is changing (as in an astronomer on a moving Earth). Astronomers must use very indirect methods to measure the distances to stars and other astronomical objects. Measuring a stars parallax is a way to find its distance. This method takes advantage of the apparent shift in position of a nearby star as it is observed from different positions as the Earth orbits the sun. Because the parallax effect depends upon the Earths motion about the sun, it is often referred to as the heliocentric parallax.

How parallax works

To understand how parallax works, hold ones thumb in front of the face. Alternately open and close each eye and notice how the thumb appears to move back and forth with respect to the background wall. Now move the thumb closer to the face and notice how this effect increases as the distance between the eyes and thumb decreases. This apparent motion (its only apparent because the thumb did not really move) is called the parallax. The brain subconsciously uses information from both eyes to estimate distances. Because the distance estimates require observation from two points, people who have lost an eye will lack this depth perception. Thus, a parallax is any apparent shift in the position of an object caused by a change in the observation position.

As Earth orbits the sun, astronomers can observe a nearby star at six-month intervals with Earth on opposite sides of the sun. The nearby star appears to move with respect to the more distant background stars. Note that the star (like the thumb) is not really moving. The parallax effect is an apparent motion caused by the motion of the observation point (either to the other eye or to the opposite side of the sun). The closer the star, the larger will be its apparent motion. This parallax, when combined with the principles of geometry and trigonometry, can be used to find the distance to stars that are relatively close. Closer stars will have a larger parallax.

Astronomers measure the parallax in the form of an angle. For even nearby stars these angles are quite small. The closest star to the sun, Proxima Centauri, has a parallax angle of less than 1 second of arc. A second of arc is 1/3600th of a degree (1°= 60 minutes of arc= 3,600 seconds of arc, 1 minute of arc= 60 seconds of arc). At a distance of 3 mi (5 km), a quarter will have an angular diameter of roughly 1 second of arc. Measuring such small angles is obviously difficult, but astronomers have managed to overcome the difficulties, detecting parallax for the first time in 1838.

The parallax angle is defined as one half of the apparent angular motion of the star as Earth orbits from one side of the sun to the opposite side. This definition is the same as the apparent motion that would be observed if the two observation points were the sun and Earth. Once this angle is measured, the distance between the sun and the star is the Earth-sun distance divided by the tangent of the parallax angle.

To simplify this calculation astronomers use a distance unit called a parsec (short for parallax-second). A parsec is the distance to a star that has a parallax angle of exactly one second of arc. One parsec is 206,265 times the distance between Earth and the Sun, 3.086 × 1013 kilometers, or 3.26 light-years (where one light-year is the distance that light travels in vacuum in one year). The distance to a star in parsecs is then simply 1 divided by the parallax angle measured in seconds of arc.

Parallax measurements

In the sixteenth century, Polish astronomer Nicolaus Copernicus (14731543) proposed that Earth and planets orbited the sun. At the time, one of the arguments proposed against the Copernican view was that there should be a heliocentric parallax if the sun was indeed the center of the solar system. However, no such parallaxes had been observed. Copernicus countered rather simply by stating that the stars were much farther away than anyone had ever imagined, so the parallax was too small to observe. When astronomers finally managed to measure a parallax, it turned out that Copernicus was right.

Astronomers did not succeed in measuring a parallax angle until 1838, when three astronomers working independently measured the parallaxes of three different stars. German mathematician and astronomer Friedrich Wilhelm Bessel (17841846) in Germany, Scottish-South African astronomer Thomas James Henderson (17981844) in South Africa, and Baltic-German astronomer Friedrich Georg Wilhelm von Struve (17931864) in Russia measured the parallaxes of the stars 61 Cygni, Alpha Centauri, and Vega, respectively.

From the ground, astronomers are now able to measure accurately parallaxes for only about 1,000 stars that are within 20 parsecs of the sun. This

KEY TERMS

Heliocentric parallax The parallax caused by the Earth orbiting the Sun.

Light-year The distance light travels in one year, roughly 9.5 trillion kilometers or 6 trillion miles.

Parallax An apparent change in position of an object caused by a change the observation position.

Parsec The distance at which a star will have a parallax angle of one second of arc, 3.26 light years.

Second of arc An angular measurement, 1/3600th of a degree.

ground-based limit requires measuring parallax angles that are as small as 1/20th of a second of arc. The quarter mentioned above is now 62 mi (100 km) away. For greater distances, astronomers must use even more indirect methods, which build on the distances found by parallax measurements. Improving the accuracy of parallax measurements will also improve the accuracy of the indirect methods that depend on parallaxes.

Earths atmosphere limits the accuracy of parallax measurements from the ground, by limiting the resolution (sharpness) of a stellar image. Sharper images, and therefore more accurate parallax measurements, require getting above Earths atmosphere. In 1989, the European Space Agency launched the Hipparcos (High Precision Parallax Collecting Satellite), with the mission of measuring the parallaxes of roughly 120,000 stars. It accomplished its goal, and was shutdown in August 1993. NASAs Hubble Space Telescope is also capable of measuring parallaxes far more accurately than they can be measured from the ground. These accurate parallax measurements from these space missions enable accurate distance measurements to a large sample of stars. Accurate distances will both help scientists attain more accurate measurements of the fundamental properties of stars, therefore increasing scientific understanding of stellar structure, and improve the accuracy of the cosmic distance scales.

Resources

BOOKS

Arny, Thomas. Explorations: An Introduction to Astronomy. Boston, MA: McGraw-Hill, 2006.

Aveni, Anthony F. Uncommon Sense: Understanding Natures Truths Across Time and Culture. Boulder, CO: University Press of Colorado, 2006.

Bacon, Dennis Henry, and Percy Seymour. A Mechanical History of the Universe. London: Philip Wilson Publishing, Ltd., 2003.

Chaisson, Eric. Astronomy: A Beginners Guide to the Universe. Upper Saddle River, NJ: Pearson/Prentice Hall, 2004.

. Astronomy Today. Upper Saddle River, NJ: Pearson/Prentice Hall, 2005.

Freedman, Roger A. Universe, Stars, and Galaxies. New York: W.H. Freeman, 2005.

Other

KidsAstronomy.com. Home page of KidsAstronomy.com. <http://www.kidsastronomy.com/> (accessed October 1, 2006).

Paul A. Heckert

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Parallax

Parallax

Astronomers must use very indirect methods to measure the distances to stars and other astronomical objects. Measuring a star's parallax is a way to find its distance. This method takes advantage of the apparent shift in position of a nearby star as it is observed from different positions as the earth orbits the Sun . Because the parallax effect depends upon the earth's motion about the Sun, it is often referred to as the heliocentric parallax.


How parallax works

To understand how parallax works, hold your thumb in front of your face. Alternately open and close each eye and notice how your thumb appears to move back and forth with respect to the background wall. Now move your thumb closer to your face and notice how this effect increases as the distance between your eyes and thumb decreases. This apparent motion (you did not really move your thumb) is called the parallax. The brain subconsciously uses information from both eyes to estimate distances. Because the distance estimates require observation from two points, people who have lost an eye will lack this depth perception . A parallax is any apparent shift in the position of an object caused by a change in the observation position.

As the earth orbits the Sun, astronomers can observe a nearby star at six-month intervals with the Earth on opposite sides of the Sun. The nearby star appears to move with respect to the more distant background stars. Note that the star (like your thumb) is not really moving. The parallax effect is an apparent motion caused by the motion of the observation point (either to the other eye or to the opposite side of the Sun). The closer the star, the larger will be its apparent motion. This parallax, when combined with the principles of geometry and trigonometry , can be used to find the distance to stars that are relatively close. Closer stars will have a larger parallax.

Astronomers measure the parallax in the form of an angle . For even nearby stars these angles are quite small. The closest star to the Sun, Proxima Centauri, has a parallax angle of less than 1 second of arc . A second of arc is 1/3600th of a degree (1°=60 minutes of arc=3600 seconds of arc, 1 minute of arc=60 seconds of arc). At a distance of 3 mi (5 km), a quarter will have an angular diameter of roughly 1 second of arc. Measuring such small angles is obviously difficult, but astronomers have managed to overcome the difficulties, detecting parallax for the first time in 1838.

The parallax angle is defined as one half of the apparent angular motion of the star as the earth orbits from one side of the Sun to the opposite side. This definition is the same as the apparent motion that would be observed if the two observation points were the Sun and Earth. Once this angle is measured, the distance between the Sun and the star is the earth-Sun distance divided by the tangent of the parallax angle.

To simplify this calculation astronomers use a distance unit called a parsec (short for parallax-second). A parsec is the distance to a star that has a parallax angle of exactly one second of arc. One parsec is 206,265 times the distance between the earth and Sun, 3.086X1013 kilometers, or 3.26 light years. The distance to a star in parsecs is then simply 1 divided by the parallax angle measured in seconds of arc.



Parallax measurements

In the sixteenth century, Copernicus proposed that the earth and planets orbited the Sun. At the time one of the arguments proposed against the Copernican view was that there should be a heliocentric parallax if the Sun was indeed the center of the solar system . At the time no such parallaxes had been observed. Copernicus countered rather simply by stating that the stars were much farther away than anyone had ever imagined, so the parallax was too small to observe. When astronomers finally managed to measure a parallax, it turned out that Copernicus was right.


Astronomers did not succeed in measuring a parallax angle until 1838, when three astronomers working independently measured the parallaxes of three different stars. Friedrich Bessel in Germany, Thomas Henderson in South Africa , and Friedrich Struve in Russia measured the parallaxes of the stars 61 Cygni, Alpha Centauri, and Vega, respectively.

From the ground, astronomers are now able to measure accurately parallaxes for only about 1,000 stars that are within 20 parsecs of the Sun. This ground based limit requires measuring parallax angles that are as small as 1/20th of a second of arc. The quarter mentioned above is now 62 mi (100 km) away. For greater distances astronomers must use even more indirect methods that build on the distances found by parallax measurements. Improving the accuracy of parallax measurements will also improve the accuracy of the indirect methods that depend on parallaxes.

The earth's atmosphere limits the accuracy of parallax measurements from the ground, by limiting the resolution (sharpness) of a stellar image. Sharper images, and therefore more accurate parallax measurements, require getting above the earth's atmosphere. In 1989, the European Space Agency launched the Hipparcos satellite , with the mission of measuring the parallaxes of roughly 120,000 stars. The Hubble Space Telescope is also capable of measuring parallaxes far more accurately than they can be measured from the ground. Accurate parallax measurements from these space missions enable accurate distance measurements to a much larger sample of stars. Accurate distances will both help us attain more accurate measurements of the fundamental properties of stars, therefore increasing our understanding of stellar structure , and improve the accuracy of our cosmic distance scales.


Resources

books

Bacon, Dennis Henry, and Percy Seymour. A Mechanical History of the Universe. London: Philip Wilson Publishing, Ltd., 2003.

Introduction to Astronomy and Astrophysics. 4th ed. New York: Harcourt Brace, 1997.

Morrison, David, Sidney Wolff, and Andrew Fraknoi. Abell's Exploration of the Universe. 7th ed. Philadelphia: Saunders College Publishing, 1995.

Zeilik, Michael, Stephen Gregory, and Elske Smith. Introductory Astronomy and Astrophysics. Philadelphia: Saunders, 1992.

periodicals

Marschall, Laurence, A., Steven J. Ratcliff, and Thomas J. Balonek. "Parallax You Can See." Sky & Telescope 84, (December 1992): 626-29.


Paul A. Heckert

KEY TERMS

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Heliocentric parallax

—The parallax caused by the Earth Orbiting the Sun.

Light year

—The distance light travels in one year, roughly 9.5 trillion kilometers or 6 trillion miles.

Parallax

—An apparent change in position of an object caused by a change the observation position.

Parsec

—The distance at which a star will have a parallax angle of one second of arc, 3.26 light years.

Second of Arc

—An angular measurement, 1/3600th of a degree.

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